Draw the bending-moment diagram for the shaft and then, from this diagram, sketch the deflection or elastic curve for the shaft's centerline. Determine the equations of the elastic curve using the coordinates \(x_{1}\) and \(x_{2}\). Use the method of integration. \(E I\) is constant.

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A -12 in. 80 lb 80 lb 4 in. 4 in. 12 in.- B